DEA reference (lambda) network

Projects the DMUs into two dimensions with Sammon mapping and draws the DEA reference network on top: each DMU is a node coloured by efficiency status, and an edge joins unit \(r\) to a reference peer \(c\) whenever the envelopment weight \(\lambda_{rc}\) exceeds edge_threshold. Edge width is proportional to \(\lambda\), shown in the legend.

Usage

plot_io_lambda_network(
  x,
  rts = c("crs", "vrs"),
  edge_threshold = 0.1,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale, passed to compute_efficiency: "crs" or "vrs".

edge_threshold

Minimum envelopment weight for an edge to be drawn (single non-negative number, default 0.1).

labels

Which DMUs to label: "none" (default), "all" (label every DMU; ggrepel with max.overlaps = Inf), "max.overlaps" (ggrepel using max.overlaps.value), or the name/id of a single DMU to highlight just that one. Use "id" to print each DMU's row number inside its own marker.

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

transparency

Node alpha in [0, 1] (default 0.7); lower values reveal overlapping nodes.

fade

Controls the single-DMU focus view. When one DMU is given to labels, all other marks (and, for the network plots, everything outside that DMU's sub-network; for the panel biplot, the other trajectories) are faded so the chosen DMU stands out. TRUE (default) uses a sensible fade level; FALSE disables it; a single number in [0, 1] sets the alpha of the faded marks directly, where larger values fade them less (e.g. 0.4 leaves them more visible).

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Further arguments passed to sammon (e.g. niter).

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Porembski, M., Breitenstein, K., & Alpar, P. (2005). Visualizing efficiency and reference relations in data envelopment analysis with an application to the branches of a German bank. Journal of Productivity Analysis, 23(2), 203–221. doi:10.1007/s11123-005-1328-5

Sammon, J. W. (1969). A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5), 401–409. doi:10.1109/T-C.1969.222678

See also

compute_efficiency, plot_io_peer_network, sammon

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_lambda_network(df, rts = "crs")